The field of the invention is magnetic resonance imaging (“MRI”) methods and systems. More particularly, the invention relates to the production of spatially-selective RF excitation pulses using parallel RF transmit systems.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the nuclei in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) that is in the x-y plane and that is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment M. A signal is emitted by the excited nuclei or “spins”, after the excitation signal B1 is terminated, and this signal may be received and processed to form an image.
When utilizing these “MR” signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received MR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
The measurement cycle used to acquire each MR signal is performed under the direction of a pulse sequence produced by a pulse sequencer. Clinically available MRI systems store a library of such pulse sequences that can be prescribed to meet the needs of many different clinical applications. Research MRI systems include a library of clinically-proven pulse sequences and they also enable the development of new pulse sequences.
The MR signals acquired with an MRI system are signal samples of the subject of the examination in Fourier space, or what is often referred to in the art as “k-space”. Each MR measurement cycle, or pulse sequence, typically samples a portion of k-space along a sampling trajectory characteristic of that pulse sequence. Most pulse sequences sample k-space in a raster scan-like pattern sometimes referred to as a “spin-warp”, a “Fourier”, a “rectilinear”, or a “Cartesian” scan. The spin-warp scan technique employs a variable amplitude phase encoding magnetic field gradient pulse prior to the acquisition of MR spin-echo signals to phase encode spatial information in the direction of this gradient. In a two-dimensional implementation (“2DFT”), for example, spatial information is encoded in one direction by applying a phase encoding gradient, Gy, along that direction, and then a spin-echo signal is acquired in the presence of a readout magnetic field gradient, Gx, in a direction orthogonal to the phase encoding direction. The readout gradient present during the spin-echo acquisition encodes spatial information in the orthogonal direction. In a typical 2DFT pulse sequence, the magnitude of the phase encoding gradient pulse, Gy, is incremented, ΔGy, in the sequence of measurement cycles, or “views” that are acquired during the scan to produce a set of k-space MR data from which an entire image can be reconstructed.
There are many other k-space sampling patterns used by MRI systems. These include “radial,” or “projection reconstruction” scans, in which k-space is sampled as a set of radial sampling trajectories extending from the center of k-space. The pulse sequences for a radial scan are characterized by the lack of a phase encoding gradient and the presence of a readout gradient that changes direction from one pulse sequence view to the next. There are also many k-space sampling methods that are closely related to the radial scan and that sample along a curved k-space sampling trajectory rather than the straight line radial trajectory.
An image is reconstructed from the acquired k-space data by transforming the k-space data set to an image space data set. There are many different methods for performing this task and the method used is often determined by the technique used to acquire the k-space data. With a Cartesian grid of k-space data that results from a 2D or 3D spin-warp acquisition, for example, the most common reconstruction method used is an inverse Fourier transformation (“2DFT” or “3DFT”) along each of the 2 or 3 axes of the data set. With a radial k-space data set and its variations, the most common reconstruction method includes “regridding” the k-space samples to create a Cartesian grid of k-space samples and then performing a 2DFT or 3DFT on the regridded k-space data set. In the alternative, a radial k-space data set can also be transformed to Radon space by performing a 1 DFT of each radial projection view and then transforming the Radon space data set to image space by performing a filtered backprojection.
Hardware costs and complexity typically limit the number of transmit channels available for use in parallel transmission MRI. Thus, in sharp contrast to parallel reception MRI, where 32 channel receive systems are available in the clinic and 128 channels systems are available for research, the most advanced parallel transmission systems typically only have P=8 channels. As a result, there are often fewer radiofrequency (“RF”) transmitters available than there are RF coil array elements, and a decision must be made as to how the transmitters are to drive the more numerous RF coil array elements. The number of choices can be very large considering that linear combinations of RF coil array elements, rather than just a single coil element, can be driven by each RF transmitter. For example, there are upwards of 12,870 possible ways to connect 8 RF transmitters to a 16 element coil array. Moreover, the RF excitation field produced by a multi-element coil array is dependent on its structure. For example, the spatial information in a transmission array having N=16 RF excitation coil elements is determined by the B1 magnetic field pattern produced by each of those coils. Thus, the ability of a parallel transmission system to take advantage of this information depends on the degree to which these B1 field patterns are spatially distinct and provide non-redundant spatial information to the RF excitation.
One way of analyzing the utility of the spatial information provided by a particular coil array for parallel transmission applications is to perform a principle component analysis (“PCA”) on the spatial profiles of the coil elements. PCA is a method that analyzes the linear combinations of the spatial profiles and forms a set of linear combinations, referred to as the “modes” of the coil array, that are orthogonal. Formally, such orthogonal profiles are the eigenvectors of a covariance matrix that represents inter-profile and intra-profile relations among the original set of spatial profiles. As a result, these orthogonal modes are sometimes referred to as “eigenmodes.” As a byproduct of the PCA method, a set of eigenvalues are produced that show the relative amount of RF energy contributed by each spatial mode. In the case where all modes contribute equally, that is, where the eigenvalues are all essentially equal in magnitude, the N-channel coil array is able to accelerate the transmit k-space trajectory N-fold. However, if, for example, an N=16 channel array has only five eigenmodes that have eigenvalues significantly greater than zero, then the array is only capable of accelerating the trajectory by a factor of five. This analysis has been used to analyze the spatial encoding power of arrays for accelerated imaging encoding on the data acquisition and image reconstruction side of the MR imaging experiment.
While PCA provides an effective method for determining optimal linear combinations of coil array spatial profiles that provide non-redundant spatial information, the method does not provide any information on how to build a hardware device that produces these non-redundant linear combinations. In practice, coil array elements are utilized as they are positioned in a coil array, or linear combinations of the analog outputs of the elements can be generated using a device such as a Butler matrix, which is described, for example, by J. Butler and R. Lowe in “Beamforming Matrix Simplifies Design of Electronically Scanned Antennas,” Electron. Design, 1961; 9:170-173.
A Butler matrix produces a spatial basis set that is useful when dealing with common transmit array geometries. Using the Butler matrix type of RF transmit array, it is fairly straightforward, and inexpensive, to expand the number of elements on an RF coil array; therefore, many different modes are made available. However, while a large number of spatial mode profiles are available, adding additional RF transmit excitation channels to drive these modes is extremely costly. Each transmit channel, which is able to drive only a single mode profile, requires a digital RF generator, a high power RF amplifier, and a specific absorption rate safety monitor.
It would therefore be desirable to provide a method for identifying and forming linear combinations of spatial modes of an RF coil array having a limited number of RF transmission channels. Furthermore, it would be desirable to provide a method for selecting subsets of these modes such that they can be driven with the limited number of available RF transmit channels in order to form a user-defined spatially-tailored RF excitation pattern. In this manner, it would be possible to achieve greater parallel transmission acceleration while limiting the number of transmit coil elements.